If you actually asked how to build pcem with static linking instead of dynamic linking, I looked briefly and I don't see any simple way to do it.
You might be able to build it with one of the manually written Makefiles (inside the src folder) and modify the LIBS= definition to include the options -Bstatic or -Bdynamic as needed.

I get no errors installing, but I find gcc in /mingw32/bin/gcc.exe which isn't in the path. I'd have expected that to be added automatically (and I've re-started MSYS2, even run it as administrator and re-installed).

Shall I just add that, or is there something else subtly different since the guide was written?

Please forgive my silly question, I saw all those $ shell commands that looked like linux

That's because MSYS2 is basically a stripped down linux distribution (Arch I believe) compiled to run on windows. It contains a linux shell, package manager, and all the *nix programs one would expect to compile software in the *nix manner (./configure, make etc.)